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At least 181 records · Page 10

An algorithm for domain decomposition in finite element analysis

A simple and efficient algorithm is described for automatic decomposition of an arbitrary finite element domain into a specified number of subdomains for finite element and substructuring analysis in a multiprocessor computer environment. The algorithm is designed to balance the work loads, to minimize the communication among processors and to minimize the bandwidths of the resulting system of equations. Small- to large-scale finite element models, which have two-node elements (truss, beam element), three-node elements (triangular element) and four-node elements (quadrilateral element), are solved on the Convex computer to illustrate the effectiveness of the proposed algorithm. A FORTRAN computer program is also included.

Al-Nasra, M.↗

Hierarchical flux-based thermal-structural finite element analysis method

A hierarchical flux-based finite element method is developed for both a one and two dimensional thermal structural analyses. Derivation of the finite element equations is presented. The resulting finite element matrices associated with the flux based formulation are evaluated in a closed form. The hierarchical finite elements include additional degrees of freedom in the approximation of the element variable distributions by the use of nodeless variables. The nodeless variables offer increased solution accuracy without the need for defining actual nodes and rediscretizing the finite element model. Thermal and structural responses are obtained from a conventional linear finite element method and exact solutions. Results show that the hierarchical flux-based method can provide improved thermal and structural solution accuracy with fewer elements when compared to results for the conventional linear element method.

Polesky, Sandra P.↗

ANSYS duplicate finite-element checker routine

An ANSYS finite-element code routine to check for duplicated elements within the volume of a three-dimensional (3D) finite-element mesh was developed. The routine developed is used for checking floating elements within a mesh, identically duplicated elements, and intersecting elements with a common face. A space shuttle main engine alternate turbopump development high pressure oxidizer turbopump finite-element model check using the developed subroutine is discussed. Finally, recommendations are provided for duplicate element checking of 3D finite-element models.

Ortega, R.↗

A unified multigrid solver for the Navier-Stokes equations on mixed element meshes

A unified multigrid solution technique is presented for solving the Euler and Reynolds-averaged Navier-Stokes equations on unstructured meshes using mixed elements consisting of triangles and quadrilaterals in two dimensions, and of hexahedra, pyramids, prisms, and tetrahedra in three dimensions. While the use of mixed elements is by no means a novel idea, the contribution of the paper lies in the formulation of a complete solution technique which can handle structured grids, block structured grids, and unstructured grids of tetrahedra or mixed elements without any modification. This is achieved by discretizing the full Navier-Stokes equations on tetrahedral elements, and the thin layer version of these equations on other types of elements, while using a single edge-based data-structure to construct the discretization over all element types. An agglomeration multigrid algorithm, which naturally handles meshes of any types of elements, is employed to accelerate convergence. An automatic algorithm which reduces the complexity of a given triangular or tetrahedral mesh by merging candidate triangular or tetrahedral elements into quadrilateral or prismatic elements is also described. The gains in computational efficiency afforded by the use of non-simplicial meshes over fully tetrahedral meshes are demonstrated through several examples.

Mavriplis, D. J.↗

Assumed--stress hybrid elements with drilling degrees of freedom for nonlinear analysis of composite structures

The goal of this research project is to develop assumed-stress hybrid elements with rotational degrees of freedom for analyzing composite structures. During the first year of the three-year activity, the effort was directed to further assess the AQ4 shell element and its extensions to buckling and free vibration problems. In addition, the development of a compatible 2-node beam element was to be accomplished. The extensions and new developments were implemented in the Computational Structural Mechanics Testbed COMET. An assessment was performed to verify the implementation and to assess the performance of these elements in terms of accuracy. During the second and third years, extensions to geometrically nonlinear problems were developed and tested. This effort involved working with the nonlinear solution strategy as well as the nonlinear formulation for the elements. This research has resulted in the development and implementation of two additional element processors (ES22 for the beam element and ES24 for the shell elements) in COMET. The software was developed using a SUN workstation and has been ported to the NASA Langley Convex named blackbird. Both element processors are now part of the baseline version of COMET.

Knight, Norman F., Jr.↗

Element Partitioning Constraints on Formation and Composition of the Earth's Core

Element partitioning study provides a number of constraints on the formation and composition of the core. First, partitioning of siderophile elements between the core and mantle should explain the "excess" siderophile elements in the mantle. Second, partitioning of light element(s) between the core and mantle should supply the core with the right amount of light element(s) to account for the density deficit in the core. Third, partitioning of light element(s) between the inner and outer core should be consistent with the observed difference in density deficits (relative to pure Fe) between these two reservoirs. In this study, high-pressure and high-temperature experiments have been conducted to investigate the pressure, temperature, and composition effects on partitioning of siderophile elements Ni and Co between core-forming Fe alloy and mantle silicate melt and minerals, partitioning of light elements S, O, and Si between core-forming Fe alloy and mantle silicate melt and minerals, and partitioning of light elements S and C between solid and liquid Fe. The implications of these results for mechanism of core formation and the composition of the core are discussed.

Li, J.↗

Thermally Mobile Trace Elements in Carbonaceous Chondrites from Cold and Hot Deserts

Some decades ago, Anders and co-workers used RNAA to classify a number of trace elements as being volatile during nebular condensation and accretion into primitive objects based upon their strong depletion in (equilibrated) ordinary chondrites relative to C1 chondrites. Such elements, e.g. Ag, Bi, Cd, Cs, In, Se, Te, Tl, Zn and others, exhibit nearly constant, C1-normalized atomic abundances in C2 (CM2) and in C3 chondrites. They interpreted the near-constancy of these abundances according to a 2-component model in which volatiles were introduced into carbonaceous (and other) chondrites as Cl material which was diluted with differing proportions of high-temperature (i.e. volatile-free) components. In this view, mean volatile element abundances of 0.48 in C2 and 0.24-0.29 x C1 in C3 chondrites indicated that C2 and C3 chondrites are, respectively, about 1:1 and 1:2-3 mixtures of Cl-like and high temperature materials. More recently, C1 normalized abundances of such volatile elements are nearly constant in most C2-6 chondrites (i.e. 25 non-Antarctic meteorites, nearly all falls, and 36 Antarctic finds) consistent with a 2- component mixing model. However, rather than being quantized, mean volatile element contents in each chondrite define a continuum from 0.92-0.14 x Cl for these 61 chondrites. A few carbonaceous chondrites - the first having been the NIPR consortium samples B-7904, Y-82162 and Y-86720 - show an altered pattern: many of the volatile elements in each exhibit the usual constancy of C1-normalized atomic abundances, but modified by further depletion of Cd and other elements like Tl and Bi. These are the most mobile trace elements, i.e. those most readily vaporized and lost from primitive meteorites during week-long heating at greater than or equal to 400 C under low ambient pressures (initially 10 (exp -5) atm H2), simulating metamorphic conditions in a primitive parent body. Similarities between mobile element data for B-7904, Y-82162 and Y-86720 with those for Murchison heated at 500-700 C suggest that these Antarctic C1 and C2-like chondrites were metamorphosed at temperatures like these in the interiors of their parent bodies. Metamorphic temperatures inferred from RNAA data and textural/mineralogic alterations are internally consistent, agreeing with those evident in heated Murchison samples. These 3 chondrites were also heated late in their histories since all have lost cosmogenic 3-He, presumably during close solar approach, and B-7904 and Y-86720 seem also to have lost substantial proportions of radiogenic He-4 and Ar-40, cf. data. Similarities in spectral reflectance data for C-, G-, B- and F- asteroids, for these meteorites and for heated Murchison samples suggest that thermally metamorphosed interior materials in these asteroids were excavated by impacts and re-deposited on them, forming their present surfaces. Establishment of the thermal metamorphic histories of carbonaceouis chondrites, then, is essential to establishing the evolution and present-day nature of C-type and related asteroids.

Lipschutz, M. E.↗

Thermally Mobile Trace Elements in Carbonaceous Chondrites From Cold and Hot Deserts

Some decades ago, Anders and co-workers used RNAA to classify a number of trace elements as being volatile during nebular condensation and accretion into primitive objects based upon their strong depletion in (equilibrated) ordinary chondrites relative to C1 chondrites. Such elements, e.g. Ag, Bi, Cd, Cs, In, Se, Te, Tl, Zn and others, exhibit nearly constant, C1-normalized atomic abundances in C2 (CM2) and in C3 chondrites. They interpreted the near-constancy of these abundances according to a 2-component model in which volatiles were introduced into carbonaceous (and other) chondrites as C1 material which was diluted with differing proportions of high-temperature (i.e. volatile-free) components. In this view, mean volatile element abundances of 0.48 in C2 and 0.24-0.29 x C1 in C3 chondrites indicated that C2 and C3 chondrites are, respectively, about 1:1 and 1:2-3 mixtures of C1-like and high temperature materials. More recently, Xiao and Lipschutz found that C-normalized abundances of such volatile elements are nearly constant in most C2-6 chondrites (i.e. 25 non-Antarctic meteorites, nearly all falls, and 36 Antarctic finds) consistent with a 2-component mixing model. However, rather than being quantized, mean volatile element contents in each chondrite define a continuum from 0.92-0.14 x C1 for these 61 chondrites. A few carbonaceous chondrites, the first having been the NIPR consortium samples B-7904, Y-82162 and Y-86720, show an altered pattern: many of the volatile elements in each exhibit the usual constancy of C1-normalized atomic abundances, but modified by further depletion of Cd and other elements like Tl and Bi. These are the most mobile trace elements, i.e. those most readily vaporized and lost from primitive meteorites during week-long heating at greater than or equal to 400 C under low ambient pressures (initially 10(exp -5) atm H2), simulating metamorphic conditions in a primitive parent body. Similarities between mobile element data for B-7904, Y-82162 and Y-86720 with those for Murchison heated at 500-700 C, suggest that these Antarctic C1 - and C2-like chondrites were metamorphosed at temperatures like these in the interiors of their parent bodies. Metamorphic temperatures inferred from RNAA data and textural/mineralogic alterations are internally consistent, agreeing., with those evident in heated Murchison samples. These 3 chondrites were also heated late in their histories since all have lost cosmogenic He-3, presumably during close solar approach, and B-7904 and Y-86720 seem also to have lost substantial proportions of radiogenic He-4 and Ar-40 cf. data in. Similarities in spectral reflectance data for C-, G-, B- and F- asteroids, for these meteorites and for heated Murchison samples suggest that thermally metamorphosed interior materials in these asteroids were excavated by impacts and re-deposited on them, forming their present surfaces. Establishment of the thermal metamorphic histories of carbonaceous chondrites, then, is essential to establishing the evolution and present-day nature of C-type and related asteroids.

Lipschutz, M. E.↗

Dependence of the Element Patterns of HYDROSTAR on Mutual Coupling

HYDROSTAR is a hybrid synthesis radiometer, intended for spaceborne applications, which employs a real aperture (waveguide stick antenna) for resolution along track and employs aperture synthesis to obtain resolution across track. This L-band system is an extension of the successful aircraft prototype, the Electronically Steered Thinned Array Radiometer (ESTAR). A proof-of-concept, full size system was constructed (45 wavelength in the synthesis direction) and subjected to extensive antenna pattern and associated microwave component measurements in an outdoor antenna test facility. HYDROSTAR employs a thinned array of 16 elements each 5.8 inches long in the along track dimension and spanning 9.5 inches across track. Each element is a narrow-wall shunt slot array with 36 slots. The polarization is linear (along-track). In the across track dimension, the antennas are deployed in a minimum redundancy array which has 90 independent baselines spaced in integer multiples of half a wavelength. The closest spacings used are for the first three elements at each end, which are spaced by only one-half wavelength. This study was intended to assess how closely each of 16 stick element patterns compare with their nominal values (as an individual, isolated radiator), when installed in their intended composite thinned array configuration. Extensive pattern measurements of the 16 elements that constitute the HYDROSTAR antenna subsystem were conducted to observe their relative features along the synthesis plane. Data was also collected for the mutual coupling between pairs of selected antennas. All antenna patterns had features different from that of an isolated element indicating some level of interaction among neighboring radiators. Those elements which had nearest neighbors at least five wavelengths away were located near the middle of the array. Their radiation patterns displayed sonic small, symmetric ripple across their full azimuth range. The patterns of elements that lie within 2.5 wavelengths of their neighbors showed stronger and asymmetric features. These are believed to be caused by mutual coupling among these structures. Evidence for this was seen when an antenna position was displaced by 0.05 wavelengths, Its pattern and those of its near neighbors were seen to change. Displacement within the plane of the array were observed to have different effects than displacements out-of-plane. A program of data analysis and theoretical development is in progress to provide a physical interpretation of the properties of these antenna patterns and to develop methods which can optimize the performance of this synthetic aperture imaging system. This includes compensation for pattern asymmetries and element position perturbation.

Weissman, David E.↗

Finite Element A Posteriori Error Estimation for Heat Conduction

This research investigates residual-based a posteriori error estimates for finite element approximations of heat conduction in single-layer and multi-layered materials. The finite element approximation, based upon hierarchical modelling combined with p-version finite elements, is described with specific application to a two-dimensional, steady state, heat-conduction problem. Element error indicators are determined by solving an element equation for the error with the element residual as a source, and a global error estimate in the energy norm is computed by collecting the element contributions. Numerical results of the performance of the error estimate are presented by comparisons to the actual error. Two methods are discussed and compared for approximating the element boundary flux. The equilibrated flux method provides more accurate results for estimating the error than the average flux method. The error estimation is applied to multi-layered materials with a modification to the equilibrated flux method to approximate the discontinuous flux along a boundary at the material interfaces. A directional error indicator is developed which distinguishes between the hierarchical modeling error and the finite element error. Numerical results are presented for single-layered materials which show that the directional indicators accurately determine which contribution to the total error dominates.

Lang, Christapher G.↗

Finite Element Modeling of the Buckling Response of Sandwich Panels

A comparative study of different modeling approaches for predicting sandwich panel buckling response is described. The study considers sandwich panels with anisotropic face sheets and a very thick core. Results from conventional analytical solutions for sandwich panel overall buckling and face-sheet-wrinkling type modes are compared with solutions obtained using different finite element modeling approaches. Finite element solutions are obtained using layered shell element models, with and without transverse shear flexibility, layered shell/solid element models, with shell elements for the face sheets and solid elements for the core, and sandwich models using a recently developed specialty sandwich element. Convergence characteristics of the shell/solid and sandwich element modeling approaches with respect to in-plane and through-the-thickness discretization, are demonstrated. Results of the study indicate that the specialty sandwich element provides an accurate and effective modeling approach for predicting both overall and localized sandwich panel buckling response. Furthermore, results indicate that anisotropy of the face sheets, along with the ratio of principle elastic moduli, affect the buckling response and these effects may not be represented accurately by analytical solutions. Modeling recommendations are also provided.

Rose, Cheryl A.↗

Low impedance printed circuit radiating element

A printed circuit radiating element comprises a geometrically symmetric planar area of a conducting material separated from a ground plane by a dielectric medium. The driving point of the radiating element is at the base of a notch in one side thereof so that the driving impedance is reduced from that obtained when the element is driven at its edge. Symmetrically disposed on opposite sides of an axis of symmetry of the element along which the driving point lies are two notches which restore the electrical symmetry of the radiating element thereby to suppress higher order modes. The suppression of these higher order modes results in a radiation pattern with minimal cross-polarized energy in the principal planes and high port-to-port isolation which could not be achieved with an asymmetrical element. Two driving points may be employed with the radiating element to produce a dual linearly polarized antenna and a reactive combiner or hybrid may be employed to obtain circularly-polarized radiations. The shape of the radiating element may be square, rectangular or circular, for example, in accordance with the desired characteristics. A plurality of radiating elements may be interconnected via appropriate transmission paths to form an antenna array.

Rahm, James K.↗

Reconfigurable Microwave Phase Delay Element for Frequency Reference and Phase-Shifter Applications

A technique was developed to provide a reconfigurable high-precision micro - wave electrical phase delay for resonators and phase shifters. The invention employs multiple branches of transmission lines with open-ended or ground-ended terminations as configurable bits or digits. This technique minimizes the errors due to limited precision of switching devices. In addition, the proposed linear analytical approach significantly produces a much simpler design than that of other prior inventions at the time of this reporting. Microwave components such as filters, phase delay elements, or resonators require a method that can accurately adjust their frequency responses. Most tuning techniques offer very wide frequency tuning range; however, it is often difficult and expensive to tune their response in a very narrow operating frequency, especially when the tuning element reaches its minimum discrete step due to fabrication tolerances. The problem becomes worse as the operating frequency is in mm-wave frequency range (>26 GHz). The electrical tuning sensitivity of a microwave line is dependent on the position of the tuning element with respect to the reference termination. By placing this tuning element away from this reference with the main transmission line connecting the two elements together the sensitivity of the tuning element can change significantly. This concept can be used in the system that requires multiple tuning sensitivities. In this case, multiple tuning branches are superimposed in the main transmission line. The proposed invention allows the transmission-line electrical length to be accurately programmed using switching elements that have limited accuracy. The invention consists of multiple branches of transmission lines connected to discrete switching devices with open-ended terminations. They are used as discrete tuning elements. These elements are connected to the main microwave transmission line and are separated by a well-defined electrical degree spacing. Each branch is programmed to have different electrical degree sensitivity, such as a combination of discrete steps in each branch, which results in a reflective line with a unique effective phase response. To reduce the number of switching devices, it is desirable to program the devices in binary configuration where each branch represents one bit in the base-2 number system. This invention allows the transmission line electrical length to be tuned precisely with customizable sensitivity based on the known sensitivity of the base tuning circuit. The tuning resolution is dependent on the distance among tuning branches.

Hsieh, Wen-Ting↗

Volatile Siderophile Elements in Shergottites: Constraints on Core Formation and Magmatic Degassing

Volatile siderophile elements (e.g., As, Sb, Ge, Ga, In, Bi, Zn, Cd, Sn, Cu, Pb) can place constraints both on early differentiation as well as the origin of volatiles. This large group of elements has been used to constrain Earth accretion [1,2], and Earth-Moon geochemistry [3]. Application to Earth has been fostered by new experimental studies of these elements such as Ge, In, and Ga [4,5,6]. Application to Mars has been limited by the lack of data for many of these elements on martian meteorites. Many volatile elements are considered in the pioneering work by [7] but for only the small number of martian samples then available. We have made new measurements on a variety of martian meteorites in order to obtain more substantial datasets for these elements using the analytical approach of [8]. We use the new dataset, together with published data from the literature, to define martian mantle abundances of volatile siderophile elements. Then, we evaluate the possibility that these abundances could have been set by mid-mantle (14 GPa, 2100 C) metal-silicate equilibrium, as suggested by the moderately and slightly siderophile elements [9]. Finally, we examine the possibility that some elements were affected by volatility and magmatic degassing.

Righter, Kevin↗

A Synthesis of Experimental Data Describing the Partitioning of Moderately Volatile Elements in Major Rock Forming Minerals: Implications for the Moon

Highly volatile elements [condensation temperatures below about 700 K] and water are highly informative about lunar bulk composition (hence origin), differentiation and magmatic evolution, and the role of impacts in delivering volatiles to the Moon. Fractionation of volatile elements compared to moderately volatile and refractory elements are informative about high-temperature conditions that operated in the proto-lunar disk. Existing data show clearly that the Moon is depleted in volatile elements compared to the bulk silicate Earth. For example, K/Th is ~400-700 in the Moon compared to 2800-3000 in Earth. A complicating factor is that the abundances of the highly volatile elements in major lunar lithologies vary by approximately two orders of magnitude. Perhaps most interesting, H2O is not correlated with the concentration of volatile elements, indicating a decoupling of highly volatile elements from the even more volatile H2O. We contend that this decoupling could be a significant tracer of processes operating during lunar formation, differentiation, and bombardment, and the combination of analyzing both volatile elements and water is likely to provide significant insight into lunar geochemical history. This variation and lack of correlation raises the question: what were the relative contributions of crystallization in the magma ocean, subsequent mantle overturn, production of secondary magmas, and addition of volatiles by large impacts in producing this apparently large range in volatile abundances? This current study will produce new partitioning data relevant to the role and distribution of the volatile and non-volatile, yet geochemically significant elements (Co, Ni, Zn, Se, Rb, Sr, Mo, Ag, Cd, In, Sb, Ce, Yb, Tl, Pb, Bi) during the thermal and magmatic evolution of the Moon.

Vander Kaaden, Kathleen E.↗

Trace Element Partitioning in the Presence of Sulfur Under Reduced Conditions

Oxygen fugacity (fO2) plays an important role in thephysicochemical properties of that system because fO2 has asubstantial impact on the partitioning behavior between andsolubility of elements in various phases. The reduced nature ofMercury and the aubrite parent bodies (APB) have raised manyquestions regarding the geochemical behavior of typicallylithophile, heat-producing, and rare-earth elements (REE) inmagmas at low fO2. In fact, interpretations of magmaticprocesses on reduced rocky bodies are difficult at presentbecause of the small number of experimental studies relevant tothe extremely low fO2 and high sulfur content of Mercury andthe APB, and our only natural analogs are the highly reducedenstatite chondrites and aubrites [e.g., 1]. Preliminaryobservations suggest that major and minor elements exhibitdifferent geochemical affinities in highly reduced, S-richsystems compared to terrestrial rocks. The partitioning behavior of major, minor, and traceelements between silicate melt, sulfide melt, and metal underhighly reduced conditions will be determined in a suite of super-liquidus experiments at a range of pressures (1 bar to 4 GPa) atNASA Johnson Space Center (JSC). Based on previous studies,heat-producing elements U and Th become more chalcophile,while K becomes less chalcophile, with more reducingconditions [2]. The nominally lithophile elements Mg and Cabecoming more chalcophile and appear as minor elements in(Fe,Mg,Ca)-S with more reducing conditions [3]. Additionally, itappears that nominally siderophile elements become moresiderophile and chalcophile with more reducing conditions,although the partitioning behavior into Mg- and Ca-bearingsulfide melts, rather than FeS, is less understood. Current workis focused on investigating elements for which we currently haveMESSENGER data as well as a host of geochemically relevanttrace elements such as REE.

Brendan A Anzures↗

Bulk Elemental Composition of Aggregate Material From Asteroid Bennu

On September 24, 2023, NASA’s OSIRIS-REx mission returned pristine carbonaceous material from asteroid Bennu. One key aspect required to understand this returned material is to establish its bulk chemical composition. This is primarily due to each chondrite group having a distinct elemental composition, which is important both as a classification tool and for establishing the connections between the different chondrite groups. As the carbonaceous and non-carbonaceous chondrites are thought to have formed in the inner and outer protoplanetary disk, respectively, measuring the bulk elemental composition of Bennu material will help test the mission hypothesis that “Bennu's parent body formed beyond the snow line by accretion of material in the protoplanetary disk”. In addition, two further mission hypotheses — paraphrased as Bennu’s bulk elemental composition reflects that of its parent asteroid and is similar to the composition of the Sun and Bennu’s dominant lithologies are comparable in composition to the most aqueously altered carbonaceous chondrites — can be directly tested by bulk elemental analyses. Elemental analyses were undertaken on sample OREX-803015-0, a 20.66 mg aggregate sourced from inside the sample collector. All analyses were conducted using an iCAP Q ICP-MS. Overall, all 54 elements analyzed for the Bennu aggregate sample show similar abundances to those of the average CI chondrite, and thus the solar photosphere composition and some of the most aqueously altered carbonaceous chondrites. The elemental data also show that Bennu is indeed a carbonaceous asteroid that formed beyond the snow line by accretion of material in the protoplanetary disk. This Bennu aggregate sample appears similar in elemental composition to samples of asteroid Ryugu, yet without the small refractory element enrichments seen in Ryugu.

P Koefoed↗

Placing three-dimensional isoparametric elements into NASTRAN

Linear (8 node), parabolic (20 node), cubic (32 node) and mixed (some edges linear, some parabolic and some cubic) have been inserted into NASTRAN, level 15.1. First the dummy element feature was used to check out the stiffness matrix generation routines for the linear element in NASTRAN. Then, the necessary modules of NASTRAN were modified to include the new family of elements. The matrix assembly was changed so that the stiffness matrix of each isoparametric element is only generated once as the time to generate these higher order elements tends to be much longer than the other elements in NASTRAN. This paper presents some of the experiences and difficulties of inserting a new element or family of elements into NASTRAN.

Newman, M. B.↗